// Copyright [2020] <unknown>
#include <bits/stdc++.h>
using namespace std;
// #define ONLINE_JUDGE
#ifndef ONLINE_JUDGE
#define dbg(x...) { cerr << "\033[32;1m" << #x << " -> "; err(x); }
void err() { cerr << "\033[39;0m" << endl; }
template<typename T, typename... A>
void err(T a, A... x) { cerr << a << ' '; err(x...); }
#else
#define dbg(...)
#endif

#define sz(x) ((int)x.size())

typedef long long LL;


const int N = 2e5+50;
int n, a[N], k;
int main(int argc, char const *argv[]) {
    // code
    scanf("%d%d", &n, &k);
    for (int i=0; i<k; ++i) {
        scanf("%d", &a[i]);
    }
    int mx = 0;
    a[k] = n + a[0];
    for (int i=0; i<k; ++i)
        mx = max(mx, a[i+1]-a[i]);
    cout << n - mx << endl;
    return 0;
}
